This proposal aims to develop population genetic theory and statistical methods for single nucleotide polymorphism (SNP) data. Theoretical methods will center on efficient generation of the history of samples of SNP genotypes using coalescent theory, and will lead to calculations of probabilities of observed patterns of SNPs. Statistical methods will include a treatment of the bias introduced when SNPs are discovered on the basis of small samples, and will also consider the estimation of the parameter theta, which is four times the product of the effective population size and the mutation rate. Tests of differences in SNP profiles from different populations will be developed and will be relevant to disease association studies. The statistical procedures developed by the proposed work will be incorporated into a computer package and made freely available.